How to build a cylinder from 2 vertices?
This is a bit complex but here goes.
in edit mode:
Select one vertex
snap the 3Dcursor to vertex with (Shift s - snap to selected)
exit edit mode
create a circle of the desired diameter and fill with triangle fan. (Shift a) The middle vertex of the triangle fan is needed later for snapping.
select the other vertex (in edit mode in the object with the vertex)
again snap the 3Dcursor to vertex
create an empty (Shift a)
select the circle
add an object constraint: track to
and select the empty as the target
The circle should now be perpendicular to the line between the two vertices.
now select the circle and enter edit mode of the circle
enable snap to vertex
and finally extrude the circle towards the second vertex.
if needed you can join the objects to create a single mesh.
I home that helps,
Cheers